Shift in the velocity of a front due to a cutoff

被引:362
作者
Brunet, E
Derrida, B
机构
[1] Laboratoire de Physique Statistique ENS, Paris, 75005
关键词
D O I
10.1103/PhysRevE.56.2597
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We consider the effect of a small cutoff epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cutoff epsilon is to select a single velocity that converges when epsilon-->0 to the one predicted by the marginal stability argument. For small epsilon, the shift in velocity has the form K(ln epsilon)(-2) and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite-size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.
引用
收藏
页码:2597 / 2604
页数:8
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